Weakley County Tn Apartments For Rent . 2 beds • 2 baths • 1,080 sq. In addition to the rent cost, you need to also account for costs of basic utilities consisting of water, garbage, electric and natural gas. 360 Parham Rd, Martin, TN 38237 MLS 42613 Trulia from www.trulia.com Prices, specials, features and availability subject to change. See floorplans, pictures, prices & info for available rental homes, condos, and townhomes in weakley county, tn. New weakley county apartments available now.